Hedging Options on Asset Portfolios against Just One Underlying Asset in the Presence of Transaction Costs

Paper: arXiv 2509.07718

Authors: Erina Nanyonga, Matt Davison

Abstract

Options are contingent claims regarding the value of underlying assets. The Black-Scholes formula provides a road map for pricing these options in a risk-neutral setting, justified by a delta hedging argument in which countervailing positions of appropriate size are taken in the underlying asset. However, what if an underlying asset is expensive to trade? It might be better to hedge with a different, but related asset that is cheaper to trade. This study considers this question in a setting in which the option written on a portfolio containing $α$ shares of one asset $S_{t_1}$ and $(1-α)$ shares of another security $S_{t_2}$ correlated with $S_{t_1}$. We suppose that the asset is hedged against only one of $S_{t_1}$ or $S_{t_2}.$ In the case of $α=0~\text{or}~1$ we can consider this model to cover the case where an option on one asset is hedged against either the right" (underlying) asset or thewrong" (related, different) asset. We hedge our portfolio on simulated data using varying trading intervals, correlation coefficients, $ρ$ and transaction costs. We calculated the risk-adjusted values ($RAV$) as the risk and return measures to make meaningful decisions on when to trade $S_{t_1}$ or $S_{t_2}.$ From the conclusions made based on $RAV,$ the size of the market price of risk and that of transaction costs on both assets are key to making a decision while hedging. From our results, trading the wrong asset can be opted for when $ρ$ is very high for reasonably small transaction costs for either of the assets.

Complexity vs Empirical Score

• Math Complexity: 5.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a decent theoretical setup for proxy-hedging a two-asset option portfolio using only one component asset under transaction costs and correlated geometric Brownian motion. However, its empirical rigor relies primarily on Monte Carlo simulations rather than empirical backtests on real market data.

Research Flowchart

  flowchart TD
    A[Research Goal: Hedging Portfolio Options via Single Asset under Transaction Costs] --> B[Inputs: Simulated Data, Correlation ρ, Trading Intervals, Transaction Costs]
    B --> C[Setup: Option on Portfolio α S1 + 1-α S2 Hedged using S1 or S2]
    C --> D[Delta Hedging Simulation under Black-Scholes Framework]
    D --> E[Evaluate Risk & Return via Risk-Adjusted Values RAV]
    E --> F[Key Outcome: Hedging with 'Wrong' Asset is Optimal if ρ is High and Transaction Costs are Low]

Cited References (31)

1. An Equilibrium Model of Imperfect Hedging: Transaction Costs, Heterogeneity in Risk Aversion, and Return Volatility (2025) — link
2. TRANSACTION COSTS AND MARKET IMPACT IN INVESTMENT MANAGEMENT (2024) — link
3. A Comprehensive Analysis of The Modern Portfolio Theory (2023) — link
4. Delta Hedging with Transaction Costs: Dynamic Multiscale Strategy using Neural Nets (2021) — link
5. Rebalancing with transaction costs: theory, simulations, and actual data (2019) — link
6. Hedge or Rebalance: Optimal Risk Management with Transaction Costs (2018) — link
7. Hedging efficiently under correlation (2017) — link
8. Trading Strategies, Portfolio Monitoring, and Rebalancing (2013) — link

0 of 31 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.